Geodesic
The Fractal Dimension of Sets Derived from Complex Bases
Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 495-500

Voir la notice de l'article provenant de la source Cambridge University Press

For each positive integer n, the radix representation of the complex numbers in the base —n + i gives rise to a tiling of the plane. Each tile consists of all the complex numbers representable in the base -n + i with a fixed integer part. We show that the fractal dimension of the boundary of each tile is 2 log λn/log(n2 + 1), where λn is the positive root of λ3 - (2n - 1) λ2 - (n - 1) 2λ - (n2 + 1).
DOI : 10.4153/CMB-1986-078-1
Mots-clés : 11K55, 51M20 
Gilbert, William J. The Fractal Dimension of Sets Derived from Complex Bases. Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 495-500. doi: 10.4153/CMB-1986-078-1
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